On $$C^*$$-norms on $${{\mathbb {Z}}}_2$$-graded tensor products
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AbstractWe systematically investigate $$C^*$$ C ∗ -norms on the algebraic graded product of $${{\mathbb {Z}}}_2$$ Z 2 -graded $$C^*$$ C ∗ -algebras. This requires to single out the notion of a compatible norm, that is a norm with respect to which the product grading is bounded. We then focus on the spatial norm proving that it is minimal among all compatible $$C^*$$ C ∗ -norms. To this end, we first show that commutative $${{\mathbb {Z}}}_2$$ Z 2 -graded $$C^*$$ C ∗ -algebras enjoy a nuclearity property in the category of graded $$C^*$$ C ∗ -algebras. In addition, we provide a characterization of the extreme even states of a given graded $$C^*$$ C ∗ -algebra in terms of their restriction to its even part.
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1974 ◽
Vol 32
◽
pp. 254-255
1983 ◽
Vol 41
◽
pp. 270-271
1973 ◽
Vol 31
◽
pp. 144-145
1973 ◽
Vol 31
◽
pp. 132-133
◽
1983 ◽
Vol 41
◽
pp. 194-195
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